Synthetic aperture radar (SAR) is an attractive imaging technique because of its ability to operate under all lighting conditions and through clouds and haze. FIG. 1 illustrates an example of a collection of 2-D SAR data. An airplane flies past an area of interest while collecting radar data. The flight path is usually a straight line. The flight direction is called the azimuth. The direction normal from the flight path to the region of interest is called the range. The plane that is formed by the azimuth and range directions is the slant plane. The normal to the slant plane is the cross-plane. Processing algorithms form a high-resolution 2-D image of the region of interest by combining the information from all of the radar data. In doing so, the processing algorithms effectively synthesize an aperture that is much larger than the actual aperture of the antenna.
While successful in many applications, the 2-D form of SAR yields very limited information about the distribution of objects in the cross-plane dimension. Further, the 2-D form of SAR has limited utility in detecting and identifying objects obscured by overlying layers. FIG. 2 illustrates an example of 2-D SAR imaging of a 3-D scene that contains objects concealed by overlying foliage. The radar illuminates the scene from the left at a single elevation. The flight path is perpendicular to the plane of the page. Because a conventional SAR image is purely 2-D, the energy within a given (range, azimuth) pixel is the sum of the energy returned by all scatterers at that range and azimuth, regardless of their position in the cross-plane dimension. In three dimensions, the frequency space is a plane (as shown, for example, in FIG. 3) and the image pixels have a tubular shape (as shown, for example, in FIG. 4). Energy returned from the overlying layers (foliage, in the example of FIG. 2) is integrated with the energy returned from the objects below, which reduces the signal-to-clutter ratio of those objects. Resolution in the third dimension may be required to separate the desired signal from the clutter.
Three-dimensional SAR extends the synthetic aperture concept used in one dimension (azimuth) in conventional SAR to two dimensions (azimuth and elevation). FIG. 5 illustrates 3-D SAR imaging of a 3-D scene. The radar now illuminates the scene from the left at multiple elevations, which creates a synthetic aperture that has two dimensions instead of one. The frequency space from this type of collection contains multiple planes, as shown, for example, in FIG. 6. The resulting impulse response shows resolution in all three dimensions, as shown, for example, in FIG. 7. The returns from the overlying layers and the objects on the ground are contained in different voxels, which improves the signal-to-clutter ratio, enabling easier detection and identification of the objects. The 2-D aperture also effectively increases the coherent integration time, which improves the signal-to-noise ratio. It is noted that interferometric SAR (IFSAR), which collects data at two elevations and is sometimes referred to as 3-D SAR, is in fact a degenerate case of true 3-D SAR.
A drawback to 3-D SAR is the difficulty in obtaining sufficient 3-D sampling. In many cases there will not be enough samples to meet the Nyquist sampling rate. Furthermore, the samples will most likely not have uniform spacing. This sparse, irregular sampling will cause sidelobes and aliases in the cross-plane dimension. These aliases and sidelobes are illustrated in FIG. 8. FIG. 8 depicts a slice of a 3-D impulse response on a 35 dB log scale, with the range and cross-plane directions noted. The peak of the impulse response is in the center of the image. A region of sidelobes is adjacent to the peak. Beyond the sidelobes, where the Nyquist sampling rate is no longer met, aliases occur. In this region, the tubes from the individual passes that make up the 3-D collection are visible. The sidelobes and aliases reduce the image quality. Consequently, the need exists for techniques to mitigate sidelobes and aliases.